Problem: Simplify the following expression: $r = \dfrac{y^2 + 14y + 48}{y + 8} $
Explanation: First factor the polynomial in the numerator. $ y^2 + 14y + 48 = (y + 8)(y + 6) $ So we can rewrite the expression as: $r = \dfrac{(y + 8)(y + 6)}{y + 8} $ We can divide the numerator and denominator by $(y + 8)$ on condition that $y \neq -8$ Therefore $r = y + 6; y \neq -8$